leiden clustering explained leiden clustering explained

One of the most widely used algorithms is the Louvain algorithm10, which is reported to be among the fastest and best performing community detection algorithms11,12. Am. Int. Not. In practical applications, the Leiden algorithm convincingly outperforms the Louvain algorithm, both in terms of speed and in terms of quality of the results, as shown by the experimental analysis presented in this paper. Rev. In subsequent iterations, the percentage of disconnected communities remains fairly stable. Clustering with the Leiden Algorithm in R This package allows calling the Leiden algorithm for clustering on an igraph object from R. See the Python and Java implementations for more details: https://github.com/CWTSLeiden/networkanalysis https://github.com/vtraag/leidenalg Install 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). The property of -connectivity is a slightly stronger variant of ordinary connectivity. This is very similar to what the smart local moving algorithm does. Natl. Here is some small debugging code I wrote to find this. For larger networks and higher values of , Louvain is much slower than Leiden. Source Code (2018). See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. Mech. Modularity optimization. For both algorithms, 10 iterations were performed. 68, 984998, https://doi.org/10.1002/asi.23734 (2017). MATH Scientific Reports (Sci Rep) However, Leiden is more than 7 times faster for the Live Journal network, more than 11 times faster for the Web of Science network and more than 20 times faster for the Web UK network. Soft Matter Phys. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. This function takes a cell_data_set as input, clusters the cells using . You are using a browser version with limited support for CSS. Hence, the complex structure of empirical networks creates an even stronger need for the use of the Leiden algorithm. For this network, Leiden requires over 750 iterations on average to reach a stable iteration. As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. One of the best-known methods for community detection is called modularity3. Hence, no further improvements can be made after a stable iteration of the Louvain algorithm. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. Article The docs are here. E 84, 016114, https://doi.org/10.1103/PhysRevE.84.016114 (2011). In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. In all experiments reported here, we used a value of 0.01 for the parameter that determines the degree of randomness in the refinement phase of the Leiden algorithm. Runtime versus quality for benchmark networks. Rev. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. This makes sense, because after phase one the total size of the graph should be significantly reduced. The PyPI package leiden-clustering receives a total of 15 downloads a week. & Girvan, M. Finding and evaluating community structure in networks. These steps are repeated until the quality cannot be increased further. J. After each iteration of the Leiden algorithm, it is guaranteed that: In these properties, refers to the resolution parameter in the quality function that is optimised, which can be either modularity or CPM. Sci. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. For a full specification of the fast local move procedure, we refer to the pseudo-code of the Leiden algorithm in AlgorithmA.2 in SectionA of the Supplementary Information. This is well illustrated by figure 2 in the Leiden paper: When a community becomes disconnected like this, there is no way for Louvain to easily split it into two separate communities. Electr. That is, no subset can be moved to a different community. The classic Louvain algorithm should be avoided due to the known problem with disconnected communities. Arguments can be passed to the leidenalg implementation in Python: In particular, the resolution parameter can fine-tune the number of clusters to be detected. A new methodology for constructing a publication-level classification system of science. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. Article We gratefully acknowledge computational facilities provided by the LIACS Data Science Lab Computing Facilities through Frank Takes. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. Zenodo, https://doi.org/10.5281/zenodo.1466831 https://github.com/CWTSLeiden/networkanalysis. However, the Louvain algorithm does not consider this possibility, since it considers only individual node movements. Note that if Leiden finds subcommunities, splitting up the community is guaranteed to increase modularity. As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. In addition, to analyse whether a community is badly connected, we ran the Leiden algorithm on the subnetwork consisting of all nodes belonging to the community. and JavaScript. Eng. If we move the node to a different community, we add to the rear of the queue all neighbours of the node that do not belong to the nodes new community and that are not yet in the queue. Besides being pervasive, the problem is also sizeable. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. Hence, the community remains disconnected, unless it is merged with another community that happens to act as a bridge. However, so far this problem has never been studied for the Louvain algorithm. It partitions the data space and identifies the sub-spaces using the Apriori principle. E 92, 032801, https://doi.org/10.1103/PhysRevE.92.032801 (2015). Moreover, when no more nodes can be moved, the algorithm will aggregate the network. 2013. E Stat. (2) and m is the number of edges. Traag, V. A., Waltman, L. & van Eck, N. J. networkanalysis. V. A. Traag. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. In the aggregation phase, an aggregate network is created based on the partition obtained in the local moving phase. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. In later stages, most neighbors will belong to the same community, and its very likely that the best move for the node is to the community that most of its neighbors already belong to. We then created a certain number of edges such that a specified average degree \(\langle k\rangle \) was obtained. This package allows calling the Leiden algorithm for clustering on an igraph object from R. See the Python and Java implementations for more details: https://github.com/CWTSLeiden/networkanalysis. For each network, Table2 reports the maximal modularity obtained using the Louvain and the Leiden algorithm. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. Nevertheless, when CPM is used as the quality function, the Louvain algorithm may still find arbitrarily badly connected communities. Instead, a node may be merged with any community for which the quality function increases. However, values of within a range of roughly [0.0005, 0.1] all provide reasonable results, thus allowing for some, but not too much randomness. Four popular community detection algorithms are explained . U. S. A. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. Soc. Random moving can result in some huge speedups, since Louvain spends about 95% of its time computing the modularity gain from moving nodes. 63, 23782392, https://doi.org/10.1002/asi.22748 (2012). Analyses based on benchmark networks have only a limited value because these networks are not representative of empirical real-world networks. We used the CPM quality function. The phase one loop can be greatly accelerated by finding the nodes that have the potential to change community and only revisit those nodes. As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. Phys. An iteration of the Leiden algorithm in which the partition does not change is called a stable iteration. Yang, Z., Algesheimer, R. & Tessone, C. J. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. Soft Matter Phys. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. 1 I am using the leiden algorithm implementation in iGraph, and noticed that when I repeat clustering using the same resolution parameter, I get different results. MathSciNet To use Leiden with the Seurat pipeline for a Seurat Object object that has an SNN computed (for example with Seurat::FindClusters with save.SNN = TRUE ). PubMed Central Please Finding and Evaluating Community Structure in Networks. Phys. In addition, a node is merged with a community in \({{\mathscr{P}}}_{{\rm{refined}}}\) only if both are sufficiently well connected to their community in \({\mathscr{P}}\). leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. 4. Google Scholar. Computer Syst. Faster unfolding of communities: Speeding up the Louvain algorithm. Provided by the Springer Nature SharedIt content-sharing initiative. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. Blondel, V D, J L Guillaume, and R Lambiotte. First iteration runtime for empirical networks. In the case of modularity, communities may have significant substructure both because of the resolution limit and because of the shortcomings of Louvain. ADS This step will involve reducing the dimensionality of our data into two dimensions using uniform manifold approximation (UMAP), allowing us to visualize our cell populations as they are binned into discrete populations using Leiden clustering. performed the experimental analysis. It therefore does not guarantee -connectivity either. Nonlin. For each network, we repeated the experiment 10 times. Below, the quality of a partition is reported as \(\frac{ {\mathcal H} }{2m}\), where H is defined in Eq. leiden_clsutering is distributed under a BSD 3-Clause License (see LICENSE). 6 show that Leiden outperforms Louvain in terms of both computational time and quality of the partitions. Communities may even be internally disconnected. We start by initialising a queue with all nodes in the network. Positive values above 2 define the total number of iterations to perform, -1 has the algorithm run until it reaches its optimal clustering. For example, for the Web of Science network, the first iteration takes about 110120 seconds, while subsequent iterations require about 40 seconds. For the Amazon and IMDB networks, the first iteration of the Leiden algorithm is only about 1.6 times faster than the first iteration of the Louvain algorithm. Note that this code is designed for Seurat version 2 releases. We name our algorithm the Leiden algorithm, after the location of its authors. . Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. Sci. E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). Use Git or checkout with SVN using the web URL. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. The Louvain algorithm is illustrated in Fig. This can be a shared nearest neighbours matrix derived from a graph object. Agglomerative clustering is a bottom-up approach. Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). For the Amazon, DBLP and Web UK networks, Louvain yields on average respectively 23%, 16% and 14% badly connected communities. 2.3. The Leiden algorithm starts from a singleton partition (a). Technol. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Some of these nodes may very well act as bridges, similarly to node 0 in the above example. reviewed the manuscript. J. The differences are not very large, which is probably because both algorithms find partitions for which the quality is close to optimal, related to the issue of the degeneracy of quality functions29. E 74, 016110, https://doi.org/10.1103/PhysRevE.74.016110 (2006). The Leiden algorithm is considerably more complex than the Louvain algorithm. Is modularity with a resolution parameter equivalent to leidenalg.RBConfigurationVertexPartition? We use six empirical networks in our analysis. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. Google Scholar. The value of the resolution parameter was determined based on the so-called mixing parameter 13. The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. Article Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. A major goal of single-cell analysis is to study the cell-state heterogeneity within a sample by discovering groups within the population of cells. ADS Modules smaller than the minimum size may not be resolved through modularity optimization, even in the extreme case where they are only connected to the rest of the network through a single edge. The Beginner's Guide to Dimensionality Reduction. Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. Louvain has two phases: local moving and aggregation. ACM Trans. As can be seen in Fig. sign in J. Comput. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. In this way, Leiden implements the local moving phase more efficiently than Louvain. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. The Leiden algorithm is partly based on the previously introduced smart local move algorithm15, which itself can be seen as an improvement of the Louvain algorithm. One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. A score of -1 means that there are no edges connecting nodes within the community, and they instead all connect nodes outside the community. Thank you for visiting nature.com. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. Eur. 9, the Leiden algorithm also performs better than the Louvain algorithm in terms of the quality of the partitions that are obtained. to use Codespaces. The algorithm continues to move nodes in the rest of the network. Detecting communities in a network is therefore an important problem. Rotta, R. & Noack, A. Multilevel local search algorithms for modularity clustering. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). Phys. Nonetheless, some networks still show large differences. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. The fast local move procedure can be summarised as follows. ADS Speed of the first iteration of the Louvain and the Leiden algorithm for benchmark networks with increasingly difficult partitions (n=107). In practice, this means that small clusters can hide inside larger clusters, making their identification difficult. Unlike the Louvain algorithm, the Leiden algorithm uses a fast local move procedure in this phase. B 86 (11): 471. https://doi.org/10.1140/epjb/e2013-40829-0. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. Note that this code is . Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. 20, 172188, https://doi.org/10.1109/TKDE.2007.190689 (2008). In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. Note that nodes can be revisited several times within a single iteration of the local moving stage, as the possible increase in modularity will change as other nodes are moved to different communities. In this section, we analyse and compare the performance of the two algorithms in practice. The algorithm then moves individual nodes in the aggregate network (d). Louvain algorithm. By submitting a comment you agree to abide by our Terms and Community Guidelines. While smart local moving and multilevel refinement can improve the communities found, the next two improvements on Louvain that Ill discuss focus on the speed/efficiency of the algorithm.